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## Homework Statement

Given two moles of some gas with two atoms per molecule which has energy [itex]U=aK_{B}T[/itex].

Assume the initial pressure is [itex]P_{i}= 2[/itex] Atm and the initial volume is [itex]P_{i}= 0.001\ m^{3}[/itex].

Now we heat it in an isochoric process to [itex]2P_{i}[/itex].

What would be [itex]\Delta T[/itex]?

What would be the work required to do that?

What would be the change in the gas particles' internal energy?

## Homework Equations

[itex]U=aK_{B}T[/itex]

[itex]dU=PdS-TdV[/itex]

## The Attempt at a Solution

Well using the first law of thermodynamics, I got that under constant volume [itex]dV=0[/itex] so [itex]\frac{dQ}{dT}=\frac{\partial U}{\partial T}[/itex] so the entire energy that we spent on heating would be transferred into the gas.

What's a tricky to me is to formulate the change in temperature as a function of pressure because [itex]dV=0[/itex] so I'd really welcome a hint.

Thanks!

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